# What is the opposite and reciprocal of 6/5?

Jun 23, 2015

The opposite of $\frac{6}{5}$ is $- \frac{6}{5}$

The reciprocal of $\frac{6}{5}$ is $\frac{5}{6}$

#### Explanation:

The opposite of a number is its additive inverse.

In our example:

$\frac{6}{5} + - \frac{6}{5} = 0$

In general, the opposite of $x$ is $- x$.

If you think of these two numbers sitting on the real line, then they are on opposite sides of the origin, $0$, at the same distance.

The reciprocal of a number is its multiplicative inverse.

In our example:

$\frac{6}{5} \cdot \frac{5}{6} = 1$

In general, the reciprocal of $x$ is $\frac{1}{x}$.

Notice that the reciprocal of $0$ is undefined - $0$ has no multiplicative inverse.